An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 × 106 m. What is the mass of Planet X? (G = 6.67 × 10−11 N × m2/kg2)Select one:a.13 × 1019 kgb.4.8 × 1024 kgc.9.6 × 1024 kgd.17 × 1022 kg
Question
An object of mass 0.50 kg is transported to the surface of Planet X where the object's weight is measured to be 10 N. The radius of the planet is 4.0 × 106 m. What is the mass of Planet X? (G = 6.67 × 10−11 N × m2/kg2)Select one:a.13 × 1019 kgb.4.8 × 1024 kgc.9.6 × 1024 kgd.17 × 1022 kg
Solution
To find the mass of Planet X, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
Where: F is the gravitational force (which is equal to the weight of the object on Planet X), G is the gravitational constant, m1 and m2 are the masses of the two objects (in this case, the object and Planet X), and r is the distance between the centers of the two objects (which is equal to the radius of Planet X).
We can rearrange this formula to solve for m2 (the mass of Planet X):
m2 = F * r^2 / (G * m1)
Substituting the given values:
m2 = 10 N * (4.0 × 10^6 m)^2 / (6.67 × 10^-11 N*m^2/kg * 0.50 kg)
Solving this equation gives the mass of Planet X as approximately 9.6 × 10^24 kg. So, the correct answer is c. 9.6 × 10^24 kg.
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